Blades with decreasing exit flow angle

ABSTRACT

An axial rotor includes a plurality of blades extending from a hub that is rotatable about an axis of rotation. Each of the plurality of blades includes a blade body that extends over a span from a base to a tip. The plurality of blades defines an exit flow angle relative to a plane that is perpendicular to the axis of rotation. The exit flow angle decreases along the span from the base to the tip.

BACKGROUND

This disclosure relates to blades, such as rotor blades or stator vane blades. Rotor and stator blades are known and used in engines, pumps, turbines and the like to propel a vehicle, move a fluid or extract work from a fluid. As fluid flows around the blades, the flow can separate and decrease the operating efficiency of the blades.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically illustrates an example desalination system.

FIG. 2 illustrates an example turbopump machine.

FIG. 3 illustrates an example turbine blade of a rotor.

FIG. 4 illustrates a cross-section through a plurality of blades of a rotor showing an exit flow angle from between the blades.

DETAILED DESCRIPTION

FIG. 1 schematically illustrates selected portions of an example desalination system 20, which provides an example operating environment for a turbopump machine 22, blade 46 and vane 47 that will be described in more detail below. It is to be understood that the desalination system 20 is only an exemplary end use environment and that other systems, such as but not limited to aircraft or aerospace systems and turbine engines, will also benefit from the disclosed turbopump machine 22, blade 46 or vane 47.

In the illustrated example, the turbopump machine 22 includes a pump section 24 and a turbine section 26. The turbopump machine 22 is fluidly connected with a reverse osmosis device 28 of known construction, for the desalination of water.

In the illustrated example, feed water is received into the pump section 24, which pressurizes the feed water and moves the feed water to the reverse osmosis device 28. As an example, the reverse osmosis device 28 includes one or more membranes to separate the feed water into a low-salinity stream 30 and a saline stream 32. The saline stream 32 is fed into the turbine section 26 of the turbopump machine 22, for energy recovery.

FIG. 2 illustrates a portion of an example of the turbopump machine 22. The pump section 24 and the turbine section 26 are coupled with a rotatable shaft 40 for rotation about axis A. The pump section 24 includes an impeller 42 that is coupled to rotate with the rotatable shaft 40.

The turbine section 26 is coupled to drive the rotatable shaft 40. The turbine section 26 includes an axial rotor 44 (e.g., turbine) having a plurality of blades 46 (one shown). In this example, the turbine section 26 also includes a plurality of fixed stator vanes 47 located upstream from the axial rotor 44. The turbine section 26 may have one or more stages of blades 46, vanes 47 or both.

The turbine section 26 includes a turbine nozzle 48 upstream from the blades 46 and in communication with an inlet 50 of the turbine section 26. An outlet 52 is located downstream from the blades 46. In the example shown, the outlet 52 is an annular outlet that extends between an outer wall 54 and an inner wall 56.

For the purpose of description, FIG. 3 shows one of the blades 46 of the axial rotor 44, however, it is to be understood that the blade 46 is also representative of the vanes 47 with regard to the salient features described herein. As can be appreciated, the vanes 47 may be fixed at their radially outer tips, whereas the blades 46 are designed to rotate. Each of the blades 46 extends from a hub 58 that is rotatable about the axis A (FIG. 2). Each of the blades 46 includes a blade body 60 (e.g., airfoil-shaped body) that extends over a span S from a base 62 at the hub 58 to a tip 64. The blade body 60 also extends between a leading end 66 and a trailing end 68 and between a pressure side surface 70 and a suction side surface 72 (FIG. 4).

The blade body 60 also defines a mean camber line C (FIG. 4) that extends from the leading end 66 to the trailing end 68. The mean camber line C is the mid-thickness of the blade 46 such that, normal to the mean camber line C, there is an equal amount of blade body distance above and below the mean camber line C.

Each of the blades 46 receives a fluid flow F that splits at the nose of the leading end 66 and flows over the pressure side surface 70 and the suction side surface 72. The flow F exits from between adjacent blades 46 at an angle relative to a plane 74 that is perpendicular to the axis of rotation A or, for the vanes 47, axis around which the vanes 47 are arranged. The direction of the exit flow F can be determined through computer simulation or experimental data, for example.

In the illustrated example, the exit flow F forms an angle 76 with regard to the plane 74. Alternatively, the angle 76 can be represented as an angle to the axis A (i.e., 90° minus angle 76). The exit flow angle 76 decreases along the span S from the base 62 to the tip 64 of the blade 46. The feature of the decreasing exit flow angle 76 facilitates the control of flow through the axial rotor to reduce or eliminate flow separation near the hub 58, for example.

The reduction or elimination of flow separation near the hub 58 enhances the efficiency of the blade 46 and the turbine section 26 of the turbopump machine 22 can be operated at speeds that are more beneficial for enhancing the efficiency of the pump section 24 of the turbopump machine 22. For instance, the turbine section 26 is operated at a speed of approximately 3500-4500 revolutions per minute, such as at 4000 revolutions per minute, to drive the pump section 24 at the same speed through the common coupling with the shaft 40. At such speeds, the pump section 24 operates in a more efficient speed regime to thereby enhance the overall efficiency performance of the turbopump machine 22.

In one example, the average exit flow angle 76 over the span S is less than 12°. For example, the average exit flow angle is an integrated average over the span S.

In a further example, the decreasing exit flow angle 76 is represented as a proportional ratio of a maximum exit flow angle at the base 62 to a minimum exit flow angle at the tip 64. For instance, the proportional ratio is no greater than 2.33. The “proportional ratio” refers to the quotient of the maximum exit flow angle divided by the minimum exit flow angle, as a scalable value.

In a further example, the proportional ratio is greater than 1 and is less than or equal to 4. In other examples, the proportional ratio is 4, 2.4 or 1.67.

The above exemplary proportional ratios are achieved by establishing the exit flow angle at the base 62 to be between 12° and 20° and the exit flow angle at the tip 64 to be between 5° and 12°.

In a further embodiment, the decreasing exit flow angle 76 has a rate of decrease over the span S from the base 62 to the tip 64 that is non-linear.

In one example, the exit flow angle 76 is controlled by the geometry of the blades 46 with regard to the shape of the pressure side surface 70 and the suction side surface 72. The shape of the pressure side surface 70 and the suction side surface 72 is represented by a set of coordinates and a radii of curvature at each respective coordinate. For example, the coordinate system is a cylindrical coordinate system that includes X-coordinates along a direction that is parallel to the axis of rotation A and radial coordinates that are a function of radial distance and angle relative to a reference point in space.

Table I below shows an exemplary set of coordinates and radii of curvature at each coordinate for the blade 46 having a decreasing exit flow angle as described herein. It is to be understood that the exemplary coordinates and radii of curvature are scalable such that the given values are relative to each other for a given scale factor. By defining the coordinate values and radii at selected locations, the surfaces of the blades 46 are ascertained.

The Table values present actual blade 46 profiles in ambient, non-operating or non-hot conditions for an end use blade.

TABLE I Co- ordi- Sec- nate Radial tion Description # X-Coord. Coord. Radii 1 suction 1 0.065000318 −0.112583481 5.618000031 side from 2 0.069693290 −0.115220830 5.618000031 LE - curve 0 3 0.074823737 −0.117943175 5.618000031 4 0.080434263 −0.120724402 5.618000031 5 0.086569928 −0.123532899 5.618000031 6 0.093278728 −0.126325026 5.618000031 7 0.100611016 −0.129043564 5.618000031 8 0.108617760 −0.131614670 5.618000031 9 0.117348216 −0.133945093 5.618000031 10 0.126846194 −0.135919631 5.618000031 11 0.137145326 −0.137400031 5.618000031 12 0.148265779 −0.138226330 5.618000031 13 0.160200313 −0.138220698 5.618000031 14 0.172921583 −0.137196854 5.618000031 15 0.186368138 −0.134972095 5.618000031 16 0.200455457 −0.131381154 5.618000031 17 0.215079650 −0.126288310 5.618000031 18 0.230129391 −0.119594432 5.618000031 19 0.245496839 −0.111237586 5.618000031 20 0.261085689 −0.101188287 5.618000031 21 0.276815355 −0.089442305 5.618000031 22 0.292621374 −0.076013222 5.618000031 23 0.308453947 −0.060926266 5.618000031 24 0.324275166 −0.044214074 5.618000031 25 0.340055823 −0.025914336 5.618000031 26 0.355772793 −0.006068866 5.618000031 27 0.371406823 0.015276501 5.618000031 28 0.386940688 0.038071387 5.618000031 29 0.402358174 0.062260009 5.618000031 30 0.417643368 0.087780744 5.618000031 31 0.432779819 0.114564918 5.618000031 32 0.447750360 0.142536327 5.618000031 33 0.462537318 0.171611324 5.618000031 34 0.477122128 0.201698154 5.618000031 35 0.491485506 0.232697010 5.618000031 36 0.505607843 0.264500797 5.618000031 37 0.519469440 0.296996117 5.618000031 38 0.533065021 0.330059648 5.618000031 39 0.546459556 0.363532424 5.618000031 40 0.559657156 0.397278816 5.618000031 41 0.572605133 0.431189537 5.618000031 42 0.585260093 0.465146542 5.618000031 43 0.597582281 0.499029756 5.618000031 44 0.609536648 0.532720149 5.618000031 45 0.621092856 0.566102803 5.618000031 46 0.632225990 0.599073410 5.618000031 47 0.642915845 0.631525517 5.618000031 48 0.653147221 0.663357437 5.618000031 49 0.662909985 0.694477797 5.618000031 50 0.672198832 0.724815845 5.618000031 51 0.681012392 0.754294515 5.618000031 52 0.689353466 0.782845497 5.618000031 53 0.697228253 0.810431600 5.618000031 54 0.704645991 0.837001979 5.618000031 55 0.711618304 0.862523258 5.618000031 56 0.718159318 0.886984587 5.618000031 57 0.724284470 0.910355806 5.618000031 58 0.730010867 0.932652533 5.618000031 59 0.735356152 0.953855932 5.618000031 60 0.740338922 0.973996639 5.618000031 61 0.744977653 0.993071556 5.618000031 62 0.749291241 1.011112213 5.618000031 63 0.753298342 1.028147936 5.618000031 64 0.757017136 1.044191718 5.618000031 65 0.760465503 1.059294343 5.618000031 66 0.763660669 1.073483109 5.618000031 67 0.766619086 1.086785316 5.618000031 68 0.769356787 1.099251032 5.618000031 69 0.771889031 1.110924363 5.618000031 70 0.774229586 1.121825933 5.618000031 71 0.776392400 1.132000685 5.618000031 72 0.778390110 1.141491771 5.618000031 73 0.780234754 1.150341392 5.618000031 74 0.781908453 1.158583283 5.618000031 75 0.783462167 1.166247129 5.618000031 76 0.784905970 1.173368812 5.618000031 77 0.786246657 1.179981947 5.618000031 78 0.787490845 1.186118960 5.618000031 79 0.788644731 1.191810608 5.618000031 80 0.789714336 1.197086573 5.618000031 trailing 1 0.789714336 1.197086573 5.618000031 edge - 2 0.789917886 1.201568007 5.618000031 curve 1 3 0.788787067 1.205909133 5.618000031 4 0.786423087 1.209721804 5.618000031 5 0.783037424 1.212664962 5.618000031 6 0.778932869 1.214475274 5.618000031 7 0.774476528 1.214990854 5.618000031 8 0.770067036 1.214165688 5.618000031 9 0.766098738 1.212073445 5.618000031 10 0.762926638 1.208901286 5.618000031 11 0.760834396 1.204933047 5.618000031 pressure 1 0.760834396 1.204933047 5.618000031 side - 2 0.758890986 1.199366808 5.618000031 curve 2 3 0.756731153 1.193209171 5.618000031 4 0.754332125 1.186405063 5.618000031 5 0.751668751 1.178895593 5.618000031 6 0.748714447 1.170621157 5.618000031 7 0.745439947 1.161515594 5.618000031 8 0.741813719 1.151509404 5.618000031 9 0.737802327 1.140536427 5.618000031 10 0.733369470 1.128522754 5.618000031 11 0.728477359 1.115400434 5.618000031 12 0.723085821 1.101097465 5.618000031 13 0.717153311 1.085549712 5.618000031 14 0.710636795 1.068693519 5.618000031 15 0.703492701 1.050473332 5.618000031 16 0.695677280 1.030842900 5.618000031 17 0.687147677 1.009767294 5.618000031 18 0.677862585 0.987224758 5.618000031 19 0.667784035 0.963210702 5.618000031 20 0.656877935 0.937739253 5.618000031 21 0.645116150 0.910846651 5.618000031 22 0.632477641 0.882591307 5.618000031 23 0.618950009 0.853056550 5.618000031 24 0.604531646 0.822353303 5.618000031 25 0.589231968 0.790614545 5.618000031 26 0.573073685 0.758000076 5.618000031 27 0.556092620 0.724689305 5.618000031 28 0.538339317 0.690882921 5.618000031 29 0.519877613 0.656794429 5.618000031 30 0.500785053 0.622647643 5.618000031 31 0.481151491 0.588670969 5.618000031 32 0.461077690 0.555092037 5.618000031 33 0.440672696 0.522130072 5.618000031 34 0.420052171 0.489992142 5.618000031 35 0.399335384 0.458867610 5.618000031 36 0.378642440 0.428924143 5.618000031 37 0.358092219 0.400304586 5.618000031 38 0.337798953 0.373124361 5.618000031 39 0.317870677 0.347470969 5.618000031 40 0.298406631 0.323403537 5.618000031 41 0.279496312 0.300954282 5.618000031 42 0.261218518 0.280130506 5.618000031 43 0.243638873 0.260915518 5.618000031 44 0.226812482 0.243273884 5.618000031 45 0.210780546 0.227152109 5.618000031 46 0.195573643 0.212483868 5.618000031 47 0.181210056 0.199191704 5.618000031 48 0.167697757 0.187191188 5.618000031 49 0.155035138 0.176393047 5.618000031 50 0.143211976 0.166705981 5.618000031 51 0.132210836 0.158038929 5.618000031 52 0.122007556 0.150302216 5.618000031 53 0.112572968 0.143409699 5.618000031 54 0.103873782 0.137279347 5.618000031 55 0.095873952 0.131834269 5.618000031 56 0.088535376 0.127002731 5.618000031 57 0.081818417 0.122719280 5.618000031 58 0.075679705 0.118929714 5.618000031 59 0.070069723 0.115595981 5.618000031 60 0.065000318 0.112583481 5.618000031 leading 1 0.065000318 0.112583481 5.618000031 edge - 2 0.043013237 0.096609026 5.618000031 curve 3 3 0.024827920 0.076412261 5.618000031 4 0.011239149 0.052875906 5.618000031 5 0.002840832 0.027028596 5.618000031 6 0.000000000 0.000000004 5.618000031 7 0.002840832 −0.027028589 5.618000031 8 0.011239149 −0.052875891 5.618000031 9 0.024827920 −0.076412261 5.618000031 10 0.043013237 −0.096609026 5.618000031 11 0.065000325 −0.112583496 5.618000031 2 suction 1 0.065000318 −0.112583481 5.848999977 side from 2 0.069683179 −0.115239047 5.848999977 LE - curve 0 3 0.074791476 −0.118028820 5.848999977 4 0.080364786 −0.120941833 5.848999977 5 0.086445890 −0.123964138 5.848999977 6 0.093081519 −0.127075091 5.848999977 7 0.100321889 −0.130244657 5.848999977 8 0.108220577 −0.133432060 5.848999977 9 0.116834305 −0.136583164 5.848999977 10 0.126221716 −0.139626786 5.848999977 11 0.136441514 −0.142471209 5.848999977 12 0.147549480 −0.145000294 5.848999977 13 0.159593701 −0.147069812 5.848999977 14 0.172610804 −0.148506343 5.848999977 15 0.186613724 −0.149105951 5.848999977 16 0.201587886 −0.148640454 5.848999977 17 0.217480972 −0.146867111 5.848999977 18 0.234199509 −0.143546104 5.848999977 19 0.251611769 −0.138459995 5.848999977 20 0.269558102 −0.131433159 5.848999977 21 0.287867129 −0.122344099 5.848999977 22 0.306372851 −0.111128107 5.848999977 23 0.324927896 −0.097771138 5.848999977 24 0.343411207 −0.082298227 5.848999977 25 0.361728609 −0.064761654 5.848999977 26 0.379809737 −0.045231745 5.848999977 27 0.397604167 −0.023788195 5.848999977 28 0.415076017 −0.000517053 5.848999977 29 0.432199448 0.024491007 5.848999977 30 0.448955536 0.051141378 5.848999977 31 0.465329200 0.079334021 5.848999977 32 0.481308073 0.108963713 5.848999977 33 0.496881396 0.139919445 5.848999977 34 0.512039185 0.172083616 5.848999977 35 0.526772141 0.205332130 5.848999977 36 0.541071355 0.239534006 5.848999977 37 0.554928243 0.274552137 5.848999977 38 0.568339825 0.310243130 5.848999977 39 0.581320465 0.346456289 5.848999977 40 0.593860745 0.383038938 5.848999977 41 0.605945051 0.419847518 5.848999977 42 0.617561340 0.456734419 5.848999977 43 0.628701091 0.493553251 5.848999977 44 0.639358640 0.530159593 5.848999977 45 0.649532020 0.566416740 5.848999977 46 0.659222603 0.602199256 5.848999977 47 0.668433666 0.637384236 5.848999977 48 0.677170455 0.671854734 5.848999977 49 0.685440183 0.705501199 5.848999977 50 0.693254590 0.738245428 5.848999977 51 0.700625658 0.770009995 5.848999977 52 0.707564712 0.800711870 5.848999977 53 0.714088321 0.830313981 5.848999977 54 0.720211267 0.858767986 5.848999977 55 0.725948811 0.886033893 5.848999977 56 0.731319785 0.912110388 5.848999977 57 0.736338675 0.936964154 5.848999977 58 0.741025090 0.960617185 5.848999977 59 0.745394588 0.983061492 5.848999977 60 0.749464512 1.004315853 5.848999977 61 0.753252745 1.024414659 5.848999977 62 0.756773591 1.043362498 5.848999977 63 0.760044515 1.061209202 5.848999977 64 0.763080955 1.077992082 5.848999977 65 0.765896201 1.093732715 5.848999977 66 0.768505454 1.108484030 5.848999977 67 0.770922959 1.122297406 5.848999977 68 0.773160458 1.135204315 5.848999977 69 0.775230050 1.147246361 5.848999977 70 0.777143657 1.158472896 5.848999977 71 0.778912544 1.168931961 5.848999977 72 0.780542612 1.178668857 5.848999977 73 0.782028496 1.187719941 5.848999977 74 0.783408284 1.196124673 5.848999977 75 0.784688652 1.203923821 5.848999977 76 0.785875857 1.211155534 5.848999977 77 0.786975920 1.217856407 5.848999977 78 0.787994623 1.224061608 5.848999977 79 0.788937449 1.229804754 5.848999977 80 0.789809585 1.235117197 5.848999977 trailing 1 0.789809585 1.235117197 5.848999977 edge - 2 0.789851844 1.239603162 5.848999977 curve 1 3 0.788565755 1.243900895 5.848999977 4 0.786066294 1.247626066 5.848999977 5 0.782576978 1.250445604 5.848999977 6 0.778410017 1.252107263 5.848999977 7 0.773938000 1.252462268 5.848999977 8 0.769561052 1.251479149 5.848999977 9 0.765670538 1.249245644 5.848999977 10 0.762614489 1.245961547 5.848999977 11 0.760666251 1.241920590 5.848999977 pressure 1 0.760666251 1.241920590 5.848999977 side - 2 0.758962274 1.236412764 5.848999977 curve 2 3 0.757061601 1.230301976 5.848999977 4 0.754942298 1.223529577 5.848999977 5 0.752580404 1.216033340 5.848999977 6 0.749949753 1.207750082 5.848999977 7 0.747021735 1.198608875 5.848999977 8 0.743765056 1.188533425 5.848999977 9 0.740146101 1.177452326 5.848999977 10 0.736128330 1.165284634 5.848999977 11 0.731672883 1.151955128 5.848999977 12 0.726738095 1.137383938 5.848999977 13 0.721280158 1.121499419 5.848999977 14 0.715253115 1.104227901 5.848999977 15 0.708609581 1.085506320 5.848999977 16 0.701301098 1.065280199 5.848999977 17 0.693279028 1.043506384 5.848999977 18 0.684495747 1.020156741 5.848999977 19 0.674905539 0.995220661 5.848999977 20 0.664466023 0.968708754 5.848999977 21 0.653140068 0.940655589 5.848999977 22 0.640897214 0.911120534 5.848999977 23 0.627715528 0.880191028 5.848999977 24 0.613583982 0.847985506 5.848999977 25 0.598503053 0.814647019 5.848999977 26 0.582487822 0.780350626 5.848999977 27 0.565567613 0.745291889 5.848999977 28 0.547788203 0.709691703 5.848999977 29 0.529211164 0.673786879 5.848999977 30 0.509913921 0.637824357 5.848999977 31 0.489988685 0.602056742 5.848999977 32 0.469541043 0.566735506 5.848999977 33 0.448687464 0.532102704 5.848999977 34 0.427553087 0.498386234 5.848999977 35 0.406268507 0.465792984 5.848999977 36 0.384966493 0.434504390 5.848999977 37 0.363779098 0.404673189 5.848999977 38 0.342834175 0.376420200 5.848999977 39 0.322253317 0.349835038 5.848999977 40 0.302148938 0.324975252 5.848999977 41 0.282622218 0.301867664 5.848999977 42 0.263761491 0.280510485 5.848999977 43 0.245642006 0.260877669 5.848999977 44 0.228324383 0.242920816 5.848999977 45 0.211855575 0.226574376 5.848999977 46 0.196267828 0.211757958 5.848999977 47 0.181581303 0.198381931 5.848999977 48 0.167803183 0.186349347 5.848999977 49 0.154929906 0.175559789 5.848999977 50 0.142948002 0.165911973 5.848999977 51 0.131835893 0.157306030 5.848999977 52 0.121564880 0.149645180 5.848999977 53 0.112101071 0.142837375 5.848999977 54 0.103406280 0.136795953 5.848999977 55 0.095439196 0.131440535 5.848999977 56 0.088156857 0.126696929 5.848999977 57 0.081515469 0.122497544 5.848999977 58 0.075461298 0.118797369 5.848999977 59 0.069958746 0.115528814 5.848999977 60 0.065000318 0.112583481 5.848999977 leading 1 0.065000318 0.112583481 5.848999977 edge - 2 0.043013237 0.096609026 5.848999977 curve 3 3 0.024827920 0.076412261 5.848999977 4 0.011239149 0.052875906 5.848999977 5 0.002840832 0.027028598 5.848999977 6 0.000000000 0.000000004 5.848999977 7 0.002840832 −0.027028589 5.848999977 8 0.011239149 −0.052875891 5.848999977 9 0.024827920 −0.076412261 5.848999977 10 0.043013237 −0.096609026 5.848999977 11 0.065000325 −0.112583488 5.848999977 3 suction 1 0.065000318 −0.112583473 6.079999924 side from 2 0.069678701 −0.115246922 6.079999924 LE - curve 0 3 0.074781358 −0.118067861 6.079999924 4 0.080347024 −0.121041872 6.079999924 5 0.086417839 −0.124163195 6.079999924 6 0.093039975 −0.127420321 6.079999924 7 0.100263201 −0.130795091 6.079999924 8 0.108141482 −0.134261981 6.079999924 9 0.116732806 −0.137784272 6.079999924 10 0.126098558 −0.141311899 6.079999924 11 0.136303216 −0.144778520 6.079999924 12 0.147412822 −0.148097008 6.079999924 13 0.159492433 −0.151154816 6.079999924 14 0.172602654 −0.153809309 6.079999924 15 0.186794519 −0.155883938 6.079999924 16 0.202098608 −0.157162815 6.079999924 17 0.218519196 −0.157395437 6.079999924 18 0.236019224 −0.156299055 6.079999924 19 0.254512638 −0.153576583 6.079999924 20 0.273858577 −0.148938581 6.079999924 21 0.293867439 −0.142131463 6.079999924 22 0.314317286 −0.132962912 6.079999924 23 0.334977984 −0.121317156 6.079999924 24 0.355635315 −0.107155696 6.079999924 25 0.376107305 −0.090504102 6.079999924 26 0.396252424 −0.071434222 6.079999924 27 0.415966898 −0.050050274 6.079999924 28 0.435180366 −0.026470426 6.079999924 29 0.453847528 −0.000820583 6.079999924 30 0.471939504 0.026766026 6.079999924 31 0.489440113 0.056155618 6.079999924 32 0.506340981 0.087212466 6.079999924 33 0.522638381 0.119797148 6.079999924 34 0.538331449 0.153765604 6.079999924 35 0.553420424 0.188967407 6.079999924 36 0.567907870 0.225249484 6.079999924 37 0.581797004 0.262452513 6.079999924 38 0.595058441 0.300418377 6.079999924 39 0.607599795 0.339024514 6.079999924 40 0.619455040 0.378082097 6.079999924 41 0.630673885 0.417405099 6.079999924 42 0.641295195 0.456814915 6.079999924 43 0.651351035 0.496140510 6.079999924 44 0.660869122 0.535219252 6.079999924 45 0.669873714 0.573898256 6.079999924 46 0.678386271 0.612032056 6.079999924 47 0.686426103 0.649483085 6.079999924 48 0.694010615 0.686120212 6.079999924 49 0.701159060 0.721841574 6.079999924 50 0.707890451 0.756561875 6.079999924 51 0.714218855 0.790177643 6.079999924 52 0.720162153 0.822626352 6.079999924 53 0.725738764 0.853865266 6.079999924 54 0.730961800 0.883825183 6.079999924 55 0.735851884 0.912509620 6.079999924 56 0.740420938 0.939865828 6.079999924 57 0.744689226 0.965921819 6.079999924 58 0.748668790 0.990649462 6.079999924 59 0.752377391 1.014080763 6.079999924 60 0.755830228 1.036236644 6.079999924 61 0.759039819 1.057124853 6.079999924 62 0.762023091 1.076802135 6.079999924 63 0.764792919 1.095298290 6.079999924 64 0.767361164 1.112641692 6.079999924 65 0.769741833 1.128889203 6.079999924 66 0.771947920 1.144095778 6.079999924 67 0.773989558 1.158295393 6.079999924 68 0.775877595 1.171534777 6.079999924 69 0.777623057 1.183868885 6.079999924 70 0.779236138 1.195349813 6.079999924 71 0.780726433 1.206028104 6.079999924 72 0.782080114 1.215944052 6.079999924 73 0.783335567 1.225144029 6.079999924 74 0.784499288 1.233671904 6.079999924 75 0.785577297 1.241571546 6.079999924 76 0.786575079 1.248883367 6.079999924 77 0.787497997 1.255646586 6.079999924 78 0.788351238 1.261899114 6.079999924 79 0.789139509 1.267675638 6.079999924 80 0.789867401 1.273009658 6.079999924 trailing 1 0.789867401 1.273009658 6.079999924 edge - 2 0.789791048 1.277495027 6.079999924 curve 1 3 0.788391769 1.281757355 6.079999924 4 0.785794675 1.285415173 6.079999924 5 0.782232046 1.288141370 6.079999924 6 0.778022587 1.289692283 6.079999924 7 0.773542821 1.289929032 6.079999924 8 0.769193351 1.288830400 6.079999924 9 0.765363216 1.286494851 6.079999924 10 0.762395084 1.283131123 6.079999924 11 0.760554373 1.279040098 6.079999924 pressure 1 0.760554373 1.279040098 6.079999924 side - 2 0.759019971 1.273573279 6.079999924 curve 2 3 0.757303357 1.267492414 6.079999924 4 0.755383790 1.260737538 6.079999924 5 0.753237665 1.253242135 6.079999924 6 0.750839770 1.244939923 6.079999924 7 0.748161912 1.235756278 6.079999924 8 0.745173335 1.225608826 6.079999924 9 0.741840601 1.214421272 6.079999924 10 0.738127112 1.202107310 6.079999924 11 0.733993292 1.188583016 6.079999924 12 0.729396880 1.173763156 6.079999924 13 0.724292696 1.157568216 6.079999924 14 0.718632758 1.139915109 6.079999924 15 0.712367117 1.120734453 6.079999924 16 0.705444157 1.099963784 6.079999924 17 0.697811067 1.077551723 6.079999924 18 0.689415336 1.053462625 6.079999924 19 0.680205762 1.027680516 6.079999924 20 0.670133531 1.000211954 6.079999924 21 0.659154654 0.971089005 6.079999924 22 0.647231221 0.940371633 6.079999924 23 0.634333551 0.908148289 6.079999924 24 0.620442986 0.874544621 6.079999924 25 0.605552733 0.839711368 6.079999924 26 0.589671075 0.803836286 6.079999924 27 0.572821915 0.767129958 6.079999924 28 0.555046558 0.729830921 6.079999924 29 0.536404133 0.692196429 6.079999924 30 0.516971469 0.654495180 6.079999924 31 0.496841967 0.617002189 6.079999924 32 0.476124763 0.579991043 6.079999924 33 0.454941630 0.543725371 6.079999924 34 0.433424950 0.508452415 6.079999924 35 0.411713898 0.474396139 6.079999924 36 0.389951080 0.441751510 6.079999924 37 0.368279248 0.410681933 6.079999924 38 0.346837282 0.381315202 6.079999924 39 0.325756997 0.353742868 6.079999924 40 0.305161119 0.328022093 6.079999924 41 0.285159975 0.304175973 6.079999924 42 0.265850484 0.282197267 6.079999924 43 0.247313693 0.262050122 6.079999924 44 0.229616284 0.243677661 6.079999924 45 0.212808073 0.227002621 6.079999924 46 0.196924165 0.211934239 6.079999924 47 0.181985036 0.198371589 6.079999924 48 0.167997345 0.186207101 6.079999924 49 0.154955938 0.175330713 6.079999924 50 0.142845050 0.165632367 6.079999924 51 0.131639972 0.157004431 6.079999924 52 0.121308580 0.149343535 6.079999924 53 0.111813135 0.142551973 6.079999924 54 0.103111841 0.136538640 6.079999924 55 0.095159508 0.131219208 6.079999924 56 0.087909691 0.126516834 6.079999924 57 0.081315503 0.122361720 6.079999924 58 0.075316474 0.118712917 6.079999924 59 0.069884099 0.115485221 6.079999924 60 0.065000318 0.112583473 6.079999924 leading 1 0.065000318 0.112583473 6.079999924 edge - 2 0.043013237 0.096609026 6.079999924 curve 3 3 0.024827920 0.076412261 6.079999924 4 0.011239149 0.052875903 6.079999924 5 0.002840832 0.027028598 6.079999924 6 0.000000000 0.000000004 6.079999924 7 0.002840832 −0.027028589 6.079999924 8 0.011239149 −0.052875895 6.079999924 9 0.024827920 −0.076412261 6.079999924 10 0.043013237 −0.096609026 6.079999924 11 0.065000325 −0.112583488 6.079999924 4 suction 1 0.065000318 −0.112583481 6.310999870 side side 2 0.069677077 −0.115250342 6.310999870 from LE - 3 0.074780613 −0.118086010 6.310999870 curve 0 4 0.080349930 −0.121089011 6.310999870 5 0.086427353 −0.124257222 6.310999870 6 0.093059547 −0.127582669 6.310999870 7 0.100296699 −0.131052852 6.310999870 8 0.108193561 −0.134648085 6.310999870 9 0.116808996 −0.138338462 6.310999870 10 0.126206130 −0.142083257 6.310999870 11 0.136452019 −0.145826668 6.310999870 12 0.147616684 −0.149493843 6.310999870 13 0.159771621 −0.152986437 6.310999870 14 0.172986686 −0.156177133 6.310999870 15 0.187325358 −0.158903480 6.310999870 16 0.202840179 −0.160964578 6.310999870 17 0.219559103 −0.162114322 6.310999870 18 0.237475678 −0.162065834 6.310999870 19 0.256538033 −0.160496533 6.310999870 20 0.276630133 −0.157069609 6.310999870 21 0.297573745 −0.151461750 6.310999870 22 0.319134593 −0.143398061 6.310999870 23 0.341046154 −0.132682756 6.310999870 24 0.363038272 −0.119213216 6.310999870 25 0.384867936 −0.102976881 6.310999870 26 0.406336814 −0.084035933 6.310999870 27 0.427298248 −0.062497687 6.310999870 28 0.447650105 −0.038502797 6.310999870 29 0.467328876 −0.012201693 6.310999870 30 0.486298025 0.016249288 6.310999870 31 0.504538178 0.046688329 6.310999870 32 0.522043705 0.078958042 6.310999870 33 0.538816154 0.112898774 6.310999870 34 0.554860055 0.148343891 6.310999870 35 0.570183933 0.185127541 6.310999870 36 0.584797919 0.223079354 6.310999870 37 0.598716736 0.262021601 6.310999870 38 0.611813962 0.301830232 6.310999870 39 0.623954952 0.342352360 6.310999870 40 0.635265768 0.383356214 6.310999870 41 0.645848155 0.424637556 6.310999870 42 0.655776978 0.466000676 6.310999870 43 0.665109396 0.507258594 6.310999870 44 0.673890531 0.548233747 6.310999870 45 0.682156801 0.588757455 6.310999870 46 0.689938307 0.628669441 6.310999870 47 0.697262883 0.667833924 6.310999870 48 0.704155743 0.706133187 6.310999870 49 0.710636258 0.743439436 6.310999870 50 0.716721952 0.779635012 6.310999870 51 0.722435832 0.814667225 6.310999870 52 0.727792740 0.848443270 6.310999870 53 0.732809663 0.880905509 6.310999870 54 0.737505198 0.912029028 6.310999870 55 0.741892278 0.941759408 6.310999870 56 0.745989621 0.970106244 6.310999870 57 0.749810457 0.997047961 6.310999870 58 0.753369927 1.022592187 6.310999870 59 0.756684661 1.046775103 6.310999870 60 0.759765208 1.069587588 6.310999870 61 0.762627661 1.091083765 6.310999870 62 0.765285730 1.111306667 6.310999870 63 0.767749548 1.130273104 6.310999870 64 0.770032525 1.148041368 6.310999870 65 0.772147417 1.164671302 6.310999870 66 0.774104714 1.180207729 6.310999870 67 0.775913656 1.194689035 6.310999870 68 0.777585089 1.208175898 6.310999870 69 0.779128909 1.220725060 6.310999870 70 0.780554414 1.232392073 6.310999870 71 0.781857789 1.243225217 6.310999870 72 0.783053756 1.253269911 6.310999870 73 0.784161866 1.262576699 6.310999870 74 0.785187662 1.271192193 6.310999870 75 0.786136568 1.279161930 6.310999870 76 0.787013710 1.286528945 6.310999870 77 0.787824035 1.293334723 6.310999870 78 0.788572073 1.299617290 6.310999870 79 0.789262295 1.305414319 6.310999870 80 0.789898813 1.310760379 6.310999870 trailing 1 0.789898813 1.310760379 6.310999870 edge - 2 0.789746940 1.315243840 6.310999870 curve 1 3 0.788276076 1.319481850 6.310999870 4 0.785617769 1.323095441 6.310999870 5 0.782009721 1.325761437 6.310999870 6 0.777774751 1.327241182 6.310999870 7 0.773291588 1.327402353 6.310999870 8 0.768961251 1.326230764 6.310999870 9 0.765170991 1.323830962 6.310999870 10 0.762259960 1.320417643 6.310999870 11 0.760488391 1.316296220 6.310999870 pressure 1 0.760488391 1.316296220 6.310999870 side - 2 0.759056151 1.310841560 6.310999870 curve 2 3 0.757450759 1.304763317 6.310999870 4 0.755651832 1.297998428 6.310999870 5 0.753636658 1.290478468 6.310999870 6 0.751380086 1.282132626 6.310999870 7 0.748854756 1.272884846 6.310999870 8 0.746030152 1.262647629 6.310999870 9 0.742873013 1.251338124 6.310999870 10 0.739346802 1.238867760 6.310999870 11 0.735412061 1.225143790 6.310999870 12 0.731026113 1.210078239 6.310999870 13 0.726143062 1.193581581 6.310999870 14 0.720714092 1.175565600 6.310999870 15 0.714687943 1.155954123 6.310999870 16 0.708011150 1.134677410 6.310999870 17 0.700628638 1.111675858 6.310999870 18 0.692485273 1.086908221 6.310999870 19 0.683526278 1.060353160 6.310999870 20 0.673699200 1.032011628 6.310999870 21 0.662955761 1.001913667 6.310999870 22 0.651253462 0.970119119 6.310999870 23 0.638557792 0.936718285 6.310999870 24 0.624844790 0.901837111 6.310999870 25 0.610103130 0.865637481 6.310999870 26 0.594336033 0.828312993 6.310999870 27 0.577563703 0.790088177 6.310999870 28 0.559824109 0.751217008 6.310999870 29 0.541174054 0.711972237 6.310999870 30 0.521688998 0.672641098 6.310999870 31 0.501462698 0.633518398 6.310999870 32 0.480605513 0.594897389 6.310999870 33 0.459242046 0.557060599 6.310999870 34 0.437508464 0.520273089 6.310999870 35 0.415548891 0.484774530 6.310999870 36 0.393511653 0.450773597 6.310999870 37 0.371545762 0.418443978 6.310999870 38 0.349796653 0.387921125 6.310999870 39 0.328403026 0.359301597 6.310999870 40 0.307493716 0.332643479 6.310999870 41 0.287185103 0.307968974 6.310999870 42 0.267579705 0.285267830 6.310999870 43 0.248762965 0.264498383 6.310999870 44 0.230805591 0.245597258 6.310999870 45 0.213760048 0.228478938 6.310999870 46 0.197663710 0.213044584 6.310999870 47 0.182537928 0.199184150 6.310999870 48 0.168389589 0.186781377 6.310999870 49 0.155213460 0.175718114 6.310999870 50 0.142992556 0.165876299 6.310999870 51 0.131700754 0.157141253 6.310999870 52 0.121304184 0.149403259 6.310999870 53 0.111763082 0.142559007 6.310999870 54 0.103033490 0.136512637 6.310999870 55 0.095068179 0.131175697 6.310999870 56 0.087818384 0.126467824 6.310999870 57 0.081234992 0.122316346 6.310999870 58 0.075254180 0.118681192 6.310999870 59 0.069850191 0.115467578 6.310999870 60 0.065000318 0.112583481 6.310999870 leading 1 0.065000318 0.112583481 6.310999870 edge - 2 0.043013237 0.096609026 6.310999870 curve 3 3 0.024827920 0.076412261 6.310999870 4 0.011239149 0.052875903 6.310999870 5 0.002840832 0.027028596 6.310999870 6 0.000000000 0.000000004 6.310999870 7 0.002840832 −0.027028589 6.310999870 8 0.011239149 −0.052875895 6.310999870 9 0.024827920 −0.076412261 6.310999870 10 0.043013237 −0.096609026 6.310999870 11 0.065000325 −0.112583481 6.310999870 5 suction 1 0.065000318 −0.112583481 6.541999817 side from 2 0.069677249 −0.115250915 6.541999817 LE - curve 0 3 0.074785046 −0.118090384 6.541999817 4 0.080363460 −0.121100970 6.541999817 5 0.086455747 −0.124281093 6.541999817 6 0.093109585 −0.127623260 6.541999817 7 0.100376360 −0.131115541 6.541999817 8 0.108312190 −0.134738699 6.541999817 9 0.116977543 −0.138463199 6.541999817 10 0.126437366 −0.142248616 6.541999817 11 0.136760846 −0.146039009 6.541999817 12 0.148020461 −0.149759114 6.541999817 13 0.160290346 −0.153309450 6.541999817 14 0.173643559 −0.156560704 6.541999817 15 0.188146830 −0.159346998 6.541999817 16 0.203856081 −0.161462322 6.541999817 17 0.220802367 −0.162652895 6.541999817 18 0.238980681 −0.162621543 6.541999817 19 0.258338809 −0.161032796 6.541999817 20 0.278757930 −0.157534346 6.541999817 21 0.300052285 −0.151787356 6.541999817 22 0.321977884 −0.143503800 6.541999817 23 0.344254673 −0.132478371 6.541999817 24 0.366600215 −0.118604265 6.541999817 25 0.388762027 −0.101872034 6.541999817 26 0.410535634 −0.082345054 6.541999817 27 0.431769937 −0.060140345 6.541999817 28 0.452363402 −0.035400555 6.541999817 29 0.472252280 −0.008283799 6.541999817 30 0.491400898 0.021047115 6.541999817 31 0.509793520 0.052431632 6.541999817 32 0.527423978 0.085701466 6.541999817 33 0.544295728 0.120693207 6.541999817 34 0.560416162 0.157240450 6.541999817 35 0.575793982 0.195168555 6.541999817 36 0.590440452 0.234300911 6.541999817 37 0.604348719 0.274465650 6.541999817 38 0.617275417 0.315548867 6.541999817 39 0.629218042 0.357358843 6.541999817 40 0.640328526 0.399663031 6.541999817 41 0.650708079 0.442240119 6.541999817 42 0.660432279 0.484884381 6.541999817 43 0.669559658 0.527402937 6.541999817 44 0.678137004 0.569616377 6.541999817 45 0.686201930 0.611352801 6.541999817 46 0.693785787 0.652450442 6.541999817 47 0.700914264 0.692751646 6.541999817 48 0.707611084 0.732119381 6.541999817 49 0.713902175 0.770464182 6.541999817 50 0.719804406 0.807658553 6.541999817 51 0.725335240 0.843601882 6.541999817 52 0.730517566 0.878261030 6.541999817 53 0.735362947 0.911529899 6.541999817 54 0.739893794 0.943415642 6.541999817 55 0.744120955 0.973841250 6.541999817 56 0.748065472 1.002840281 6.541999817 57 0.751737773 1.030362606 6.541999817 58 0.755156755 1.056454539 6.541999817 59 0.758335233 1.081117511 6.541999817 60 0.761286259 1.104367375 6.541999817 61 0.764026284 1.126267076 6.541999817 62 0.766566396 1.146836996 6.541999817 63 0.768918455 1.166113257 6.541999817 64 0.771096051 1.184160948 6.541999817 65 0.773111284 1.201039433 6.541999817 66 0.774973631 1.216785312 6.541999817 67 0.776693165 1.231449723 6.541999817 68 0.778280377 1.245095134 6.541999817 69 0.779745102 1.257782340 6.541999817 70 0.781096280 1.269567847 6.541999817 71 0.782323360 1.280498266 6.541999817 72 0.783455431 1.290624499 6.541999817 73 0.784503341 1.299997807 6.541999817 74 0.785472572 1.308667421 6.541999817 75 0.786368310 1.316679597 6.541999817 76 0.787195563 1.324079275 6.541999817 77 0.787959099 1.330908895 6.541999817 78 0.788663387 1.337208629 6.541999817 79 0.789312661 1.343016267 6.541999817 80 0.789910853 1.348366976 6.541999817 trailing 1 0.789910853 1.348366976 6.541999817 edge - 2 0.789726913 1.352849364 6.541999817 curve 1 3 0.788225770 1.357076764 6.541999817 4 0.785541654 1.360671163 6.541999817 5 0.781914651 1.363311172 6.541999817 6 0.777669191 1.364760637 6.541999817 7 0.773185015 1.364889860 6.541999817 8 0.768863142 1.363687158 6.541999817 9 0.765090168 1.361260295 6.541999817 10 0.762203574 1.357826352 6.541999817 11 0.760461569 1.353692293 6.541999817 pressure 1 0.760461569 1.353692293 6.541999817 side - 2 0.759065628 1.348215222 6.541999817 curve 2 3 0.757499516 1.342105031 6.541999817 4 0.755742967 1.335296154 6.541999817 5 0.753773510 1.327717662 6.541999817 6 0.751566172 1.319296122 6.541999817 7 0.749093711 1.309952497 6.541999817 8 0.746325791 1.299597025 6.541999817 9 0.743229210 1.288140059 6.541999817 10 0.739767849 1.275492668 6.541999817 11 0.735902011 1.261554003 6.541999817 12 0.731589198 1.246234059 6.541999817 13 0.726783395 1.229434133 6.541999817 14 0.721435785 1.211063981 6.541999817 15 0.715494931 1.191041470 6.541999817 16 0.708906829 1.169287562 6.541999817 17 0.701616347 1.145739198 6.541999817 18 0.693567395 1.120350003 6.541999817 19 0.684704661 1.093093038 6.541999817 20 0.674974918 1.063966632 6.541999817 21 0.664328396 1.032995462 6.541999817 22 0.652721524 1.000238061 6.541999817 23 0.640118599 0.965788066 6.541999817 24 0.626493633 0.929770052 6.541999817 25 0.611834168 0.892353058 6.541999817 26 0.596141517 0.853734076 6.541999817 27 0.579434335 0.814150035 6.541999817 28 0.561749101 0.773862839 6.541999817 29 0.543140948 0.733157754 6.541999817 30 0.523684502 0.692337573 6.541999817 31 0.503472567 0.651712239 6.541999817 32 0.482615024 0.611590266 6.541999817 33 0.461236149 0.572270215 6.541999817 34 0.439472109 0.534031808 6.541999817 35 0.417467535 0.497129112 6.541999817 36 0.395371377 0.461783081 6.541999817 37 0.373333603 0.428178221 6.541999817 38 0.351500660 0.396458298 6.541999817 39 0.330012947 0.366726816 6.541999817 40 0.309000880 0.339046419 6.541999817 41 0.288582951 0.313441962 6.541999817 42 0.268863022 0.289902329 6.541999817 43 0.249928936 0.268385261 6.541999817 44 0.231853381 0.248824358 6.541999817 45 0.214690611 0.231129527 6.541999817 46 0.198479787 0.215196654 6.541999817 47 0.183244258 0.200910151 6.541999817 48 0.168992221 0.188147098 6.541999817 49 0.155719474 0.176782593 6.541999817 50 0.143410191 0.166692078 6.541999817 51 0.132038772 0.157754347 6.541999817 52 0.121571653 0.149853483 6.541999817 53 0.111969233 0.142880529 6.541999817 54 0.103187338 0.136734247 6.541999817 55 0.095178157 0.131321386 6.541999817 56 0.087892756 0.126557618 6.541999817 57 0.081281371 0.122366585 6.541999817 58 0.075279035 0.118705392 6.541999817 59 0.069858894 0.115477197 6.541999817 60 0.065000318 0.112583481 6.541999817 leading 1 0.065000318 0.112583481 6.541999817 edge - 2 0.043013237 0.096609026 6.541999817 curve 3 3 0.024827920 0.076412261 6.541999817 4 0.011239149 0.052875903 6.541999817 5 0.002840832 0.027028596 6.541999817 6 0.000000000 0.000000004 6.541999817 7 0.002840832 −0.027028589 6.541999817 8 0.011239149 −0.052875895 6.541999817 9 0.024827920 −0.076412261 6.541999817 10 0.043013237 −0.096609026 6.541999817 11 0.065000325 −0.112583488 6.541999817

In another example, the exit flow angle 76 is a camber angle between the mean camber line C at the trailing end 68 (as shown by extended mean camber line 77) relative to the plane 74. In one example, the flow angle 76 approaches approximately 5° and approximately 12° near the tip 64 and approaches approximately 12° and approximately 20° at the base 62 near the hub 58.

Although a combination of features is shown in the illustrated examples, not all of them need to be combined to realize the benefits of various embodiments of this disclosure. In other words, a system designed according to an embodiment of this disclosure will not necessarily include all of the features shown in any one of the Figures or all of the portions schematically shown in the Figures. Moreover, selected features of one example embodiment may be combined with selected features of other example embodiments.

The preceding description is exemplary rather than limiting in nature. Variations and modifications to the disclosed examples may become apparent to those skilled in the art that do not necessarily depart from the essence of this disclosure. The scope of legal protection given to this disclosure can only be determined by studying the following claims. 

1. An axial rotor comprising: a plurality of blades extending from a hub and arranged about an axis, each of the plurality of blades including a blade body extending over a span from a base to a tip, the plurality of blades defining an exit flow angle relative to a plane that is perpendicular to the axis of rotation, the exit flow angle decreasing along the span from the base to the tip.
 2. The axial rotor as recited in claim 1, wherein an average exit flow angle over the span is less than 12°.
 3. The axial rotor as recited in claim 1, wherein a proportional ratio of a maximum exit flow angle along the span to a minimum exit flow angle along the span is no greater than 2.33.
 4. The axial rotor as recited in claim 1, wherein the rate of decrease of the exit flow angle along the span from the base to the tip is non-linear.
 5. The axial rotor as recited in claim 1, wherein the exit flow angle at the tip is 5-12° and the exit flow angle at the base is 12-20°.
 6. The axial rotor as recited in claim 1, wherein a proportional ratio of a maximum exit flow angle at the base and a minimum exit flow angle at the tip is greater than 1 and less than or equal to
 4. 7. The axial rotor as recited in claim 1, wherein the blade body extends between a leading edge and a trailing edge and a suction side surface and a pressure side surface, the suction side surface and the pressure side surface being defined by a set of coordinates and a radii of curvature at each coordinate as set forth in Table I and scaled by a desirable factor.
 8. The axial rotor of claim 1, wherein under normal operating conditions, a fluid flow about each of the plurality of blades does not separate near the trailing edge near the hub and wherein the fluid flow about each of the plurality of blades does not separate near the trailing edge near the tip.
 9. A turbopump machine comprising: a rotatable shaft; a pump coupled to rotate with the rotatable shaft; a turbine coupled to drive the rotatable shaft, the turbine including an axial rotor having a plurality of blades extending from a hub that is rotatable about an axis of rotation, each of the plurality of blades including a blade body extending over a span from a base to a tip, the plurality of blades defining an exit flow angle relative to a plane that is perpendicular to the axis of rotation, the exit flow angle decreasing along the span from the base to the tip.
 10. A method of controlling flow over an axial rotor, the method comprising: for an axial rotor that includes a plurality of blades extending from a hub that is rotatable about an axis of rotation, each of the plurality of blades including a blade body extending over a span from a base to a tip, the plurality of blades defining an exit flow angle relative to a plane that is perpendicular to the axis of rotation, establishing a decreasing exit flow angle along the span from the base to the tip.
 11. The method as recited in claim 9, including establishing an average exit flow angle of less than 12° over the span from the base to the tip.
 12. The method as recited in claim 9, including establishing a proportional ratio of a maximum exit flow angle along the span to a minimum exit flow angle along the span that is no greater than 2.33.
 13. The method as recited in claim 9, including establishing the rate of decrease of the exit flow angle along the span from the base to the tip to be non-linear.
 14. The method as recited in claim 9, including establishing the exit flow angle at the tip to be 5-12° and the exit flow angle at the base to be 12-20°.
 15. The method as recited in claim 9, including establishing a proportional ratio of a maximum exit flow angle along the span at the base and a minimum exit flow angle at the tip to be greater than 1 and less than or equal to
 4. 16. The method as recited in claim 9, wherein the blade body extends between a leading edge and a trailing edge and a suction side surface and a pressure side surface, the suction side surface and the pressure side surface being defined by a set of coordinates and a radius of curvature at each coordinate as set forth in Table I and scaled by a desirable factor.
 17. The method as recited in claim 9, including operating the axial rotor at a speed of 3500-4500 revolutions per minute to drive a pump that coupled with the axial rotor at the same speed.
 18. An axial turbine comprising: a plurality of airfoils that extend from a hub, each of the plurality of airfoils including an airfoil body extending between a leading end, a trailing end, a base at the hub, and a tip and defining a mean camber line, wherein a camber angle of the mean camber line at the trailing end relative to a plane that is perpendicular to an axis about which the plurality of airfoils are arranged is between approximately 5° and approximately 12° near the tip and is between approximately 12° and approximately 20° near the hub.
 19. The axial turbine of claim 18, wherein under normal operating conditions, a fluid flow about each of the plurality of airfoils does not separate near the trailing edge near the hub and wherein the fluid flow about each of the plurality of airfoils does not separate near the trailing edge near the tip. 